Question

The ratio in which the sphere $x^2+y^2+z^2=504$ divides the line joining the points $(12,-4,8)$ and $(27,-9,18)$ is

• A. $-2:3$
• B. $2:3$
• C. $3:4$
• D. $1:2$

Answer 1

Answer: (A), (B)

The correct options are
A $2:3$
B $-2:3$

The ratio in which a line segment joining two points $A(x_1,y_1,z)$ and $B(x_2,y_2,z_2)$ is divided by the sphere $x^2+y^2+z^2=a^2$ is

$\lambda =\sqrt{-\left(\frac{x_1^2+y_1^2+z_1^2-a^2}{x_2^2+y_2^2+z_2^2-a^2}\right)}=\sqrt{-\left(\frac{144+16+64-504}{729+81+324-504}\right)}$

$=\sqrt{-\left(\frac{224-504}{1134-504}\right)}=\sqrt{-\left(\frac{-280}{630}\right)}$

$=\sqrt{\frac{4}{9}}=\pm 2:3$